Related papers: A Three Function Variational Principle for Station…
I consider the problem of weakly nonlinear stability of three-dimensional convective magnetohydrodynamic systems, where there is no alpha-effect or it is insignificant, to perturbations involving large scales. I assume that the convective…
This work provides a recipe for creating drag, lift and torque closures for static assemblies of axisymmetric, non-spherical particles. Apart from Reynolds number $Re$ and solids volume fraction $\epsilon_s$, we propose four additional…
The resistive magnetohydrodynamic (MHD) equations as usually defined in the quasineutral approximation refer to a system of 14 scalar equations in 14 scalar variables, hence are determined to be complete and soluble. These equations are a…
The linear marginal instability of an MHD Taylor-Couette flow of infinite vertical extension is considered. For hydrodynamically unstable flows the minimum Reynolds number exists even without a magnetic field, but there are also solutions…
With focus on anharmonic chains, we develop a nonlinear version of fluctuating hydrodynamics, in which the Euler currents are kept to second order in the deviations from equilibrium and dissipation plus noise are added. The required…
We extend recent work on hydrodynamics with global multipolar symmetries -- known as "fracton hydrodynamics" -- to systems in which the multipolar symmetries are gauged. We refer to the latter as "fracton magnetohydrodynamics", in analogy…
In the present paper, we study a new type of large-scale instability, which arises in obliquely rotating electroconductive fluids with a small-scale external force of zero helicity. This force excites small-scale velocity oscillations with…
In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincar\'e variational principle. In this geometric framework, we derive new,…
This paper concerns the rigorous periodic homogenization for a non-linear strongly coupled system, which models a suspension of magnetizable rigid particles in a non-conducting carrier viscous Newtonian fluid. The fluid drags the particles,…
In this paper, we develop a Hamiltonian variational formulation for the nonequilibrium thermodynamics of simple adiabatically closed systems that is an extension of Hamilton's phase space principle in mechanics. We introduce the…
In this work, we investigate the difference estimate for a class of Euler-Maxwell system and those of magnetohydrodynamics (in short, MHD) systems in three dimensions. We decompose the Euler-Maxwell system into three parts, namely the MHD…
The three-dimensional nonlinear dynamics of an electron gas in a semiconductor quantum well is analyzed in terms of a self-consistent fluid formulation and a variational approach. Assuming a time-dependent localized profile for the fluid…
The perturbative variational formulation of the Vlasov-Maxwell equations is presented up to third order in the perturbation analysis. From the second and third-order Lagrangian densities, respectively, the first-order and second-order…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
Ideal magnetohydrodynamic (MHD) equilibria on a Riemannian 3-manifold satisfy the stationary Euler equations for ideal fluids. A stationary solution $X$ admits a large set of ``adapted" metrics in $M$ for which $X$ solves the corresponding…
The Eulerian variational principle for the Vlasov-Poisson-Amp\`{e}re system of equations in a general coordinate system is presented. The invariance of the action integral under an arbitrary spatial coordinate transformation is used to…
We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of…
Magnetization in highly conductive plasmas is ubiquitous to astronomical systems. Flows in such media can be described by three path functions $\Lambda_\alpha$, or, for a steady flow, by two stream functions $\lambda_\kappa$ and an…
We investigate analytically the magnetic instability in a rotating and electrically conducting fluid induced by an imposed magnetic field with its associated electric current. The short-wavelength approximation is used in the linear…
We consider the evolution of arbitrarily large perturbations of a prescribed pure hydrodynamical flow of an electrically conducting fluid. We study whether the flow perturbations as well as the generated magnetic fields decay or grow with…